1

### AIPMT 2005

In a face-centered cubic lattice, a unit cell is shared equally by how many unit cells?
A
2
B
4
C
6
D
8

## Explanation

In given unit cell it is shared equally by six faces of different unit cells.
2

### AIPMT 2004

A compound formed by elements X and Y crystallises in a cubic structure in which the X atoms are at the face-centres. The formula of the compound is
A
XY3
B
X3Y
C
XY
D
XY2

## Explanation

X atoms at the corners = ${1 \over 8} \times 8$ = 1

Y atoms at the face centres = ${1 \over 2} \times 6$ = 3

Ratio of atoms, X : Y = 1 : 3

Hence, formula is XY3.
3

### AIPMT 2003

The pyknometric density of sodium chloride crystal is 2.165 $\times$ 103 kg m$-$3 while its X-ray density is 2.178 $\times$ 103 kg m$-$3. The fraction of unoccupied sites in sodium chloride crystal is
A
5.96
B
5.96 $\times$ 10$-$2
C
5.96 $\times$ 10$-$1
D
5.96 $\times$ 10$-$3

## Explanation

Molar volume from pyknometric density

= ${M \over {2.165 \times {{10}^3}}}$ m3

Molar volume from X-ray density

= ${M \over {2.178 \times {{10}^3}}}$ m3

Volume unoccupied

= ${M \over {{{10}^3}}}\left( {{1 \over {2.165}} - {1 \over {2.178}}} \right)$ m3

Fraction unoccupied

= ${{\left( {{{0.013M \times {{10}^{ - 3}}} \over {2.165 \times 2.178}}} \right)} \over {\left( {{{M \times {{10}^{ - 3}}} \over {2.165}}} \right)}}$

= 5.96 $\times$ 10-3
4

### AIPMT 2001

When Zn converts from melted state to its solid state, it has hcp structure, then find the number of nearest atoms.
A
6
B
8
C
12
D
4

## Explanation

hcp is a closed packed arrangement in which the unit cell is hexagonal and coordination number is 12.